Laser-Based Angle-Resolved Photoemission Spectroscopy of Topological Insulators The Harvard ...

117 Pages·2012·4.27 MB·English

Laser-Based Angle-Resolved Photoemission
Spectroscopy of Topological Insulators
Citation
Wang, Yihua. 2012. Laser-Based Angle-Resolved Photoemission Spectroscopy of Topological
Insulators. Doctoral dissertation, Harvard University.
Permanent link
http://nrs.harvard.edu/urn-3:HUL.InstRepos:9823978
Terms of Use
This article was downloaded from Harvard University’s DASH repository, and is made available
under the terms and conditions applicable to Other Posted Material, as set forth at http://
nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Share Your Story
The Harvard community has made this article openly available.
Please share how this access benefits you. Submit a story .
Accessibility
©2012 by Yihua Wang
All rights reserved.
Advisor: Prof. Nuh Gedik Yihua Wang

Laser-based Angle-resolved Photoemission Spectroscopy of
Topological Insulators
Abstract
Topological insulators (TI) are a new phase of matter with very exotic electronic properties on
their surface. As a direct consequence of the topological order, the surface electrons of TI form bands
that cross the Fermi surface odd number of times and are guaranteed to be metallic. They also have a
linear energy-momentum dispersion relationship that satisfies the Dirac equation and are therefore
called Dirac fermions. The surface Dirac fermions of TI are spin-polarized with the direction of the spin
locked to momentum and are immune from certain scatterings. These unique properties of surface
electrons provide a platform for utilizing TI in future spin-based electronics and quantum computation.
The surface bands of 3D TI can be directly mapped by angle-resolved photoemission
spectroscopy (ARPES) and the spin polarization can be determined by spin-resolved ARPES. These types
of experiments are the first to establish the 3D topological order, which demonstrates the power of
ARPES in probing the surface of strongly spin-orbit coupled materials. Extensive investigation of TI has
ranged from understanding the fundamental electronic and lattice structure of various TI compounds to
building TI-based devices in search of more exotic particles such as Majorana fermions and magnetic
monopoles. Surface-sensitive techniques that can efficiently disentangle the charge and spin degrees of
freedom have been crucially important in tackling the multi-faceted problems of TI.
In this thesis, I show that laser-based ARPES in combination with a time-of-flight spectrometer is
a powerful tool to study the spin structure and charge dynamics of the Dirac fermions on the surface of
iii
TI. Chapter 1 gives a brief introduction of TI. Chapter 2 describes the basic principles behind ARPES and
time-resolved ARPES (TrARPES). Chapter 3 provides a detailed account of the experimental setup to
perform laser-based ARPES and TrARPES. In Chapters 4 and 5, how these two techniques are effectively
applied to investigate two unique electronic properties of TI is elaborated. Through these studies, I have
obtained a complete mapping of the spin texture of several prototypical topological insulators and have
uncovered the cooling mechanism governing the hot surface Dirac fermions.

iv
Contents
Abstract ........................................................................................................................................................ iii
Contents ........................................................................................................................................................ v
Acknowledgement ...................................................................................................................................... vii
List of figures .............................................................................................................................................. viii
Chapter 1 Introduction to topological insulators ..................................................................................... - 1 -
1.1 Quantum Hall state and topological order ..................................................................................... - 1 -
1.2 Quantum spin Hall insulator and topological insulator .................................................................. - 2 -
Chapter 2 Theoretical background for ARPES and TrARPES ..................................................................... - 6 -
2.1 ARPES .............................................................................................................................................. - 6 -
2.2 Time-resolved ARPES .................................................................................................................... - 12 -
Chapter 3 Experimental setup ................................................................................................................ - 18 -
3.1 Overview ....................................................................................................................................... - 18 -
3.2 Ultrafast laser for TrARPES ............................................................................................................ - 20 -
3.3 Higher harmonics generation and optical parametric amplification ............................................ - 27 -
3.4 ARTOF ............................................................................................................................................ - 36 -
3.5 UHV system ................................................................................................................................... - 43 -
3.6 Sample preparation and characterization .................................................................................... - 49 -
Chapter 4 CD-ARPES on topological materials ........................................................................................ - 52 -
4.1 Introduction .................................................................................................................................. - 52 -
v
4.2 Theory of photoemission on spin-orbit coupled materials .......................................................... - 53 -
4.3 TOF-ARPES on Bi Se ..................................................................................................................... - 58 -
2 3
4.4 CD-ARPES spectra.......................................................................................................................... - 63 -
4.5 Extracting spin texture from CD-ARPES ........................................................................................ - 67 -
4.6 Characterizing and eliminating false instrumental circular dichroism ......................................... - 75 -
Chapter 5 TrARPES on topological insulators ......................................................................................... - 78 -
5.1 Introduction .................................................................................................................................. - 78 -
5.2 TrARPES spectra ............................................................................................................................ - 80 -
5.3 Fitting of TrARPES spectra ............................................................................................................. - 83 -
5.4 Electronic temperature and chemical potential dynamics ........................................................... - 88 -
5.5 Doping dependence of the temperature dynamics ...................................................................... - 94 -
Chapter 6 Conclusions ............................................................................................................................ - 99 -
Bibliography .......................................................................................................................................... - 101 -
vi
Acknowledgement
This thesis would not have been possible without the help from many wonderful people I am fortunate
enough to be surrounded by. First of all, I would like to thank my advisor Prof. Nuh Gedik at MIT. He
took me as his first graduate student when I was three years into my study and has supported me since
in every way he can. His trust and patience in me have guided me through all the challenging and
exciting projects I have embarked on. I have enjoyed working with all the members of the Gedik group
including Dr. Darius Torchinsky, Dr. David Hsieh, graduate students Dan Pilon, James McIver, Alex
Frenzel, Fahad Mahmood, Edbert Sie and Changmin Lee, and undergraduate student Gus Downs. I am
especially indebted to David because he is the first person to teach me about topological insulators and
his sharp vision on almost every topic has given me lots of inspirations to carry on the research in this
and related fields. I have also benefitted from the collaboration with other groups at MIT. Most notably,
Prof. Young Lee’s group and Prof. Pablo Jarillo-Herrero’s group have both provided me with high quality
samples. And I have also learned a lot from the frequent discussions with Prof. Liang Fu.
Everyone who has been through graduate school knows that it is a grueling process. But luckily I have
made some valuable friends during my seven years of life here in Boston. They have made these years
endurable, memorable and even enjoyable. Among them are my best friends Ou Chen and John Fei,
whose mix of batter and encouragement keep me both grounded and afloat.
At last, I want to thank my parents Deqiang Wang and Qinpin Liu. Even though they did not teach me
much physics, they have taught me a more important thing which is the right attitude to overcome any
challenge throughout my life. Their unconditional love is what has been driving me through the ups-and-
downs of my Phd. I regret not being able to be around them for such a long period of time. But I am
constantly motivated by knowing that what I am doing makes them proud.
vii
List of figures
Figure 1.1 Quantum Hall state. ................................................................................................................. - 2 -
Figure 1.2 A quantum spin Hall insulator appears with spin-orbit coupling.. .......................................... - 4 -
Figure 2.1 Energy diagram of photoelectrons. ......................................................................................... - 7 -
Figure 2.2 Schematics of the outcoming angle of photoelectrons with certain energy. .......................... - 8 -
Figure 2.3 Three-step model of a photoemission process........................................................................ - 9 -
Figure 2.4 Hemispherical energy analyzers. ........................................................................................... - 11 -
Figure 2.5 A time-resolved ARPES energy diagram ................................................................................ - 13 -
Figure 2.6 Coupling between the electron, spin and lattice degrees of freedom .................................. - 14 -
Figure 2.7 Ultrafast thermalization of electrons after photoexcitation. ................................................ - 15 -
Figure 2.8 Ultrafast electron cooling by the lattice. ............................................................................... - 16 -
Figure 3.1 Experimental setup for laser-based time-resolved ARPES .................................................... - 19 -
Figure 3.2 Wyvern optical diagram ......................................................................................................... - 21 -
Figure 3.3 A grating spectrometer .......................................................................................................... - 23 -
Figure 3.4 Optical diagram of an autocorrelator .................................................................................... - 24 -
Figure 3.5 Temporally chirped pulse ....................................................................................................... - 25 -
Figure 3.6 FROG images .......................................................................................................................... - 25 -
Figure 3.7 Prism pair compressor ........................................................................................................... - 26 -
Figure 3.8 Frequency mixing process ...................................................................................................... - 28 -
Figure 3.9 Mixed frequency generation .................................................................................................. - 29 -
Figure 3.10 SHG and THG generation ..................................................................................................... - 31 -
Figure 3.11 Index of refraction of BBO ................................................................................................... - 32 -
Figure 3.12 GVM in SHG broadens the pulsewidth ................................................................................ - 34 -
viii
Figure 3.13 DFG and OPA energy diagram .............................................................................................. - 36 -
Figure 3.14 A time-of-flight electron spectrometer for ARPES ............................................................... - 37 -
Figure 3.15 Electron trajectory in the flight tube ................................................................................... - 38 -
Figure 3.16 TOF detector ........................................................................................................................ - 39 -
Figure 3.17 Delay line detector illustration ............................................................................................ - 40 -
Figure 3.18 Hardware-Software interface .............................................................................................. - 42 -
Figure 3.19 UHV system diagram ............................................................................................................ - 44 -
Figure 3.20 Universal curve of electron mean free path in metals. ....................................................... - 45 -
Figure 3.21 Sample holder with a Bi2Se3 sample under photoexcitation .............................................. - 48 -
Figure 3.22 sample post for cleaving ...................................................................................................... - 50 -
Figure 4.1 Photon incident geometry with reference to the sample ..................................................... - 54 -
Figure 4.2 Energy-momentum intensity spectra obtained from TOF-ARPES. ........................................ - 59 -
Figure 4.3 Energy-momentum cuts through the intensity spectra along direction. ......................... - 60 -
Figure 4.4 Constant energy slice of the intensity spectra of Bi Se . ....................................................... - 60 -
2 3
Figure 4.5 Hexagonal warping effect in Bi Te ........................................................................................ - 61 -
2 3
Figure 4.6 Out-of-plane spin component in Bi2Te3 measured by spin-ARPES. ...................................... - 62 -
Figure 4.7 Energy-momentum cut from the intensity spectra ............................................................... - 63 -
Figure 4.8 Difference CD spectra of Bi2Se3 ............................................................................................ - 64 -
Figure 4.9 Cuts through the difference intensity spectra.. ..................................................................... - 65 -
Figure 4.10 Constant energy slices of the difference spectra at various sample rotation angle. .......... - 66 -
Figure 4.11 Trigonal crystal structure of Bi Se ....................................................................................... - 68 -
2 3
Figure 4.12 Three spin components from the circular-dichroism difference spectra. ........................... - 69 -
Figure 4.13 Spin polarization in the ideal helical regime. ....................................................................... - 70 -
Figure 4.14 Deformed spin texture ......................................................................................................... - 73 -
ix
Figure 4.15 Fitting of the in-plane spin modulation. .............................................................................. - 74 -
Figure 4.16 Optical diagram to compensate for the window birefringence. ......................................... - 76 -
Figure 4.17 CD difference spectra with window birefringent ................................................................ - 77 -
Figure 5.1 TrARPES on p-doped Bi2Se3. ................................................................................................. - 79 -
Figure 5.2 TrARPES on Bi2Te3. ................................................................................................................ - 80 -
Figure 5.3 TrARPES spectra at time delay t = 0 ...................................................................................... - 81 -
Figure 5.4 TrARPES spectra of Bi2Se3 ..................................................................................................... - 82 -
Figure 5.5 Momentum integrated spectra for surface and bulk states .................................................. - 83 -
Figure 5.6 Surface state spectra with different sets of parameters ....................................................... - 85 -
Figure 5.7 Agreement between data and fit of the momentum integrated intensity spectra .............. - 87 -
Figure 5.8 Electronic temperature and chemical potential dynamics for high doping sample .............. - 88 -
Figure 5.9 Electronic temperature and second harmonic generation time dependence ...................... - 89 -
Figure 5.10 Electronic temperatures and chemical potentials of SS and CB .......................................... - 91 -
Figure 5.11 The photoexcitation process................................................................................................ - 92 -
Figure 5.12 Interband inelastic electron-electron recombination rate .................................................. - 93 -
Figure 5.13 Surface doping effect. .......................................................................................................... - 95 -
Figure 5.14 Surface and bulk electronic temperature dynamics at 15 K ................................................ - 96 -
Figure 5.15 Slow component doping dependence. ................................................................................ - 97 -
x